0.8668 is the correct result if you use the formula fv=pv*(1+i)^n which is the theoretical (mathematical) compounding.

But usually for non-integer periods (like 1.5 years) banks are using mixed compounding: this method uses the above (exponential) formula only for the integer part of the period, and a linear compounding for fractional parts of the period, i.e. fv=pv*(1+i)^n1 * (1+n2*i) with n1=IP(n) and n2=FP(n).

For your example this means fv=1/((1+0.10)^1*(1+0.5*0.10))=0.8658 which is the result of the 12c. So it seems you have set your 12c to 'mixed compounding'.

BTW, in reality it's even more complicated if PV is not at the beginning of the year (or the interest period). In fact the full formula is fv=pv*(1+n1*i)*(1+i)^n2*(1+n3*i) where n1 and n3 are the fractional parts of the first and last year and n2 is the number of full years.

Example: if you pay PV=1000 at 1st April 2000 and want it back exactly 10 years later (at 5% p.a.), then you get:

FV=1000*(1+9/12*0.05)*(1+0.05)^9*(1+3/12*0.05) = 1629.62

If you want a really good TVM calculator which handles all these cases (and much more), then download TVM-Calc v16.0 from my website: ;-)

When you say that I have my hp-12c set to mixed compounding, does this mean that I can set the 12c to mathematical compounding instead of mixed compounding?

I've tried to play around with the compounding periods but I always send the PV figure way out.

I'd love to purchase your calc. but I would need to take it into an exam, which is an impossibility with an app. Thankfully all my calculations are 'in-arrears' at the moment. I think that my head would explode if I had to do them 'in-advance'.

Going back to the HP12c, I didn't remember seeing a compounding setting in the User Guide. Can anyone help??

I'm also a bit confused as to why the HP17bii uses a default theoretical compounding but the 12c doesn't.

Quote:
does this mean that I can set the 12c to mathematical compounding instead of mixed compounding?

Yes, I remember that I've read here anytime in the past that the HP-12c can be switched between those 2 different compounding method, but don't ask me how - I don't have a real 12c and I'm using the 12c emulator very seldom.

Quote:
I'd love to purchase your calc.

Well, no need to purchase anything - all my programs are freeware! ;-)

But you're right, it's a PC software, so if you aren't allowed to use a notebook then it won't help you in your exams.

I hope any 12c user can tell you how to switch this setting for the compounding method ...

Thank you so much for your assistance over this problem. As you have probably guessed I'm not very mathematically minded so your help on my simple problem is much appreciated.

From your excerpt of the User Guide I will place the HP12c into 'odd-period' mode when I've got a non-integer period calculation. For all other integer calculations I should leave it in in 'normal' mode.

Quote:
From your excerpt of the User Guide I will place the HP12c into 'odd-period' mode when I've got a non-integer period calculation. For all other integer calculations I should leave it in in 'normal' mode.

Yes, for a non-integer 'n' you can choose the method with the 'C' indicator ({STO][EEX]), i.e. either calculating the odd period with linear interest (no 'C') or with compound interest ('C').

For integer 'n' this setting (i.e. 'C' ON or OFF) should have no influence, so you could just always use this 'C' mode (if you prefer the mathematical compounding as in your first example).

Quote:Additional Explanation
The C status indicator is used in Odd-Period calculations. When interest on a cash flow begins to accrue before the beginning of the first regular payment period, it is necessary to place the HP 12C calculator in Odd-Period mode. This is done by entering a non-integer value for n. The integer portion represents the number of full periods. The fractional part specifies the length of the odd period as a fraction of the full period. The calculations during the odd period can be done with either simple or compound interest. If the C status indicator in the display is not lit, simple interest is used. Compound interest, indicated by the C in the display, is set by pressing [STO][EEX]. Pressing [STO][EEX] again returns the calculations to simple interest for the odd period.